Your Affirmation is not a petition. It is a personal expression of your basic values and it has standing in law. These include the principle that we should never harm the innocent and that everyone’s life is of equal value and should not be snuffed out at random. The Affirmations are evidence of your principled rejection of nuclear weapons.
The Public Conscience is a real concept in International Humanitarian Law. It was referred to in the 1899 and 1907 Hague Conventions, well before nuclear weapons were thought of. Among other things it codified the law applying to the use of weapons in war. The people who drew up the Conventions knew that new weapons would be developed and they found a formula which applied the law to them:
“In cases not covered by this Protocol or other international agreements, civilians and combatants remain under the protection and authority of the principles of inter-national law derived from international custom, from the principles of humanity and from the dictates of the Public Conscience